(4x+28)(6x+30)=-20

Solution for (4x+28)(6x+30)=-20 equation:

(4x+28)(6x+30)=-20

We move all terms to the left:

(4x+28)(6x+30)-(-20)=0

We add all the numbers together, and all the variables

(4x+28)(6x+30)+20=0

We multiply parentheses ..

(+24x^2+120x+168x+840)+20=0

We get rid of parentheses

24x^2+120x+168x+840+20=0

We add all the numbers together, and all the variables

24x^2+288x+860=0

a = 24; b = 288; c = +860;
Δ = b2-4ac
Δ = 2882-4·24·860
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-8\sqrt{6}}{2*24}=\frac{-288-8\sqrt{6}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+8\sqrt{6}}{2*24}=\frac{-288+8\sqrt{6}}{48}
$